Today we see the
start of a week of visits from our future S1 students. They
will work through a timetable of sample lessons given by the
various subject departments.
At Mathematics
some may even be reading this sentence at this precise
moment and are about to be shown other SENTENCES created by our present S1
students.
Their homework
will be to create their own sentences, send them to us and
if they stretch our minds into complicated enough logical
knots then we will publish them here.
Try some
excellent sets of problems for S1-S3 and S4-S6. They have a deadline of 22nd
May for sending in solutions.
In this month's Interact
Magazine our S3 students: Sam
Larg, Dave Stewart, Richard Mason, Joe Neilson, Matthew
Broadbent and Ross Craig have had their work published on
the problem Never
Prime.
Congratulations to all these
students for their excellent effort and results.
.
Links of
the Week
Figure out the Mystery
Operation at this page from the Teacher's Lab
(part of The Annenberg/CPB Math and Science Project)
"For over 350 years, some of the greatest minds
of science struggled to prove what was known as Fermat's
Last Theorem -- the idea that a certain simple equation had
no solutions. Now hear from the man who spent seven years of
his life cracking the problem, read the intriguing story of
an 18th century woman mathematician who hid her identity in
order to work on Fermat's Last Theorem, and demonstrate that
a related equation, the Pythagorean Theorem, is true." The
articles are at
NOVA
Online.
This week we
present the fascinating game of Eatcake where you devour rows of cake
slices attempting to be the last to eat. If you conquer
the strategy then try the variation Turn-and-Eatcake.... a real challenge to your
stomach!
Math
that makes you go wow is a Site
from Yale University that introduces mathematical objects
such as the sphere, the torus, the Klein bottle, the Mobius
band etc. Visually stunning with many Java Applets giving
"3D renderings" that may be rotated with your cursor
on-screen.
Most limericks aspire to this rhythm or pattern
of unstressed (u) and stressed (S) syllables.
The combinations uS and uuS are called
metrical feet. What is amazing is the occurence of the
Fibonacci Numbers (see Amazing Number Facts
No 38 and
No 54) underlying
the structure of the limerick:
1
2
3
5
8
13
21
34
1 limerick
2 short lines of 2 metrical feet
3 long lines of 3 metrical feet. 3
stressed syllables in a long line and 3 unstressed
syllables in a short line
5 syllables in a short line and 5
unstressed syllables in a long line
If you have answers,
discoveries, new questions etc to do with this Number Fact
then...E-mail us at
madrascollege.maths@fife.gov.uk
and we will publish them here.
Free
Mathematical Applications & Games for the
Mac
Tic-Mac-Toe
This is a visually
pleasing rendering of the traditional Tic-Tac-Toe or
Naughts-and-Crosses game. For those that think they have
nothing to learn from this game try the misere version
where the first to win loses! There's life in the old
games yet!!
Harcourt and Academic Press have
an extensive searchable Mathematics
Dictionary on-line, an extremely
useful reference Site to bookmark.
The Centre
for Innovation in Maths Teaching(Univ of Exeter) has recently created a
Specialist
Calculators area on their Site.
Here you may use calculators dedicated to specific tasks:
length, area, volume, mass, temperature, density, pressure
& stress, speed, fuel consumption, power etc
The University of Michigan Math
Scholars Site is hosting The
Infinily Site created by Jason
Howald. There can be no other topic that fascinates as much
as the infinite. This Site aims to be a learning resource
for high school and college students. Topics related to the
idea of infinity are discussed and there are puzzles
described as "from easy to incredibly difficult".
This amazing square of numbers
was discovered over 200 years ago by Benjamin
Franklin . It has some
remarkable properties. The sum of each of the eight rows and
each of the eight columns is 260. But look at the numbers in
each 'half-row' and in each 'half-column'. How many totals
of 130 are there? And that's not all ... look at this
pattern:
You might like to find the sum of the
red numbers first. Now add up all the light purple
numbers. Now compare these totals with the dark
blue totals. Follow this up with a quick addition
of all the green numbers. Finish off by comparing
all these totals with the yellow sum, the dark
purple sum, the light blue sum and the brown sum.
A trully amazing arrangement of numbers!
Now view the
animation!!
If you have answers,
discoveries, new questions etc to do with this Number Fact
then...E-mail us at
madrascollege.maths@fife.gov.uk
and we will publish them here.
The worksheet Fractions
& Decimals 1 investigates
recurring and terminating decimals. It uses the ability
of Mathematica to expand decimal fractions to virtually
any required accuracy. For example the command N[1/7,30]
gives the decimal expansion of 1/7 to 30 decimal
places.
.
Free
Mathematical Applications & Games for the
Mac
...It's About Prime
Generate a list of
primes at break-neck speed. Calculate the prime
factorisation of enormous numbers instantaneously. With
this power available for your classes you may be the
first to have a student who finally discovers that
elusive pattern among the primes!
In the pencil
and paper game of SNORT bulls and cows must be
carefully placed in adjoining fields but not too close!
And when it's party time Seating
Boys & Girls can be very frustrating. Keep the boys
and girls apart or you'll loose the game.
On February 25,
2000 it was announced that the Double Bubble Conjecture had
been proved. Reference to this conjecture dates back to
1873. When two soap bubbles meet and merge they form two
spherical caps separated by a third spherical cap (a flat
disc if the bubbles contain equal volumes) all of which meet
at 120 degree angles. It is the fact that this arrangement
provides the least-perimeter (ie surface area) way of
enclosing the two original volumes that has now been proved
mathematically
Our student
Sue Liu (S5) has been selected along with 19 other
students from the UK to attend a Mathematical Olympiad
Training course at Cambridge University during the Easter
holidays. The selection was as a result of her success in
The British Maths Olympiad Rounds 1 and 2.
Congratulations to Sue on this great achievement.
Stefan Waner and Steven
Costenoble from Hofstra University have created a set of
high quality on-line tutorial Web Pages. They consist of
clear exposition with useful animations and are supplemented
with excellent sets of exercises. Of use in particular to
Scottish teachers at this revision time are:
Leonardo
of Pisa wondered how
many pairs of rabbits would be produced in the
nth
generation starting from a single pair of rabbits and
assuming that any pair of rabbits from one generation
produces one pair of rabbits for the next generation and
a further pair of rabbits for the generation after that,
and then they die.
This picture shows the
first two generations and what they produce:
The diagrams become
more complicated but here are the next two generations
and some of their offsprings:
So far the numbers
produced in each generation are as follows:
generation 1
generation 2
generation 3
generation 4
generation 5
1
1
2
3
5
Try to draw a diagram
showing the numbers produced in generations 6 and 7.
There is an easier way to produce the "Rabbit Numbers"
sequence. Can you discover it?
[This Amazing Number
Fact is dedicated to Class 1H at Madras College, St
Andrews (99-00)]
If you have answers,
discoveries, new questions etc to do with this Number Fact
then...E-mail us at
madrascollege.maths@fife.gov.uk
and we will publish them here.
This weekend
400 Scottish Maths Teachers attending the Scottish
Mathematical Council's Conference at the University of
Stirling will be entertained by Johnny Ball when he
delivers the opening address. We give a few links to
illustrate the activities of this amazing man:
This
month's problems suitable for S1-S3 and S4-S6 have a deadline of 22nd
April for solutions. Many of last month's problems
became Tough
Nuts with
no solutions being sent in by the deadline. They can
still be tackled... get solving!
Congratulations to Claire Kruithof
(S3) from Madras College for her work on Happy
Octopus. which appeared in
this month's Interact
Magazine.
.
Free
Mathematical Applications & Games for the
Mac
This clock
has a great world map display illustrating the current
extent of darkness on the globe. It can display four
clocks (conventional or digital) showing times in four
selectable places around the world. An animation
facility takes you through a complete day ... try it
with the sundial display selected and watch the shadow
change! A highly educational demonstration for 24-hour
clock and time work within the Maths Classroom.
What do the following
square numbers have in common?
118622 = 139854276
123632 = 152843769
125432 = 157326849
146762 = 215384976
156812 = 245893761
159632 = 254817369
180722 = 326597184
190232 = 361874529
193772 = 375468129
If you are still not sure
then calculate these ones for yourself:
195692
196292
203162
228872
230192
231782
234392
242372
242762
244412
248072
250592
255722
259412
264092
267332
271292
272732
290342
291062
There are exactly 30 square
numbers with this amazing property. All but one of them
are given above. The remaining nine digit square begins
92*******. Can you find it?
And then of course
there are: 320432,
322862,
331442 ..
What's amazing about these? Can you find more?
If you have answers,
discoveries, new questions etc to do with this Number Fact
then...E-mail us at
madrascollege.maths@fife.gov.uk
and we will publish them here.
Revision
Tests and Tutorials Although
designed for SAT Tests these on-line explanatory sample
test questions cover much of the Standard Grade Credit
syllabus and some Higher work.
Illuminations. This excellent Site comes from the National
Council of Teachers of Mathematics. The aim is to provide
internet resources to improve the teaching and learning
of mathematics for all students and in particular to
"illuminate" the new NCTM Principles
and Standards for School Mathematics.
On-Line
Math Applications is a
wonderful Site from California created by six
eleven/twelve year old students and two teachers.
We continue with our series
of resource material for using the powerful Mathematica
software in the classroom. This week's offering is
Crossnumber
1: a cross-number puzzle which
involves questions about powers of two that are too large
for a normal calculator.
.
Amazing Number Fact No 52
Counting to Infinity and
Beyond
When you count a set of
objects you are in effect labelling them:
Let's use this second
way of labelling when we try to count an infinite number
of objects:
The number of objects
is given by the next label to be used. This label cannot
be any of our 'nomal' finite numbers. The label used is
the greek letter omega: . So we have counted objects so far. Now we have a surprise in
store:
But try counting the
objects the other way round:
Since the last label
used is then you have counted to +1 which is the next label to be used. So
counting beyond our normal finite numbers into the
transfinite numbers springs an amazing surprise:
You might like to
figure out the meaning of 2 x and x 2 . Are they the
same?
If you have answers,
discoveries, new questions etc to do with this Number Fact
then...E-mail us at
madrascollege.maths@fife.gov.uk
and we will publish them here.
..Mathematica in the Classroom..
...
. So we have counted 
